As the present day understanding of freezing and related phenomena has already a history of almost
thirty years, it is certainly useful to be aware of a broader context of the problem under consideration.
To this end it is appropriate to mention that an extreme "toy model" case of the problem in hand is
represented by the famous Random Energy Model (REM) by Derrida
where the freezing phenomenon was discovered and investigated for the first time [1]}, [2]}.
The REM in some loose sense can be looked at as a limiting
"zero-dimensional" \(N=0\)  case of the model we studied elsewhere in this set of lectures.
It amounts essentially to replacing the logarithmically correlated random potential by a
collection of \(M\)  uncorrelated Gaussian variables with the variances chosen to be scaled
with \(M\)  in the same way as in the logarithmic case: \(<V_i^2>=2g^2\ln {M}\) .
REM is simple enough to allow explicit calculation of the free energy by direct counting of degrees of freedom,
and the result essentially coincides with (REF ).
A very informative account of the REM problem can be found in the fifth chapter of [3]}.
